Variational Integrals on Orlicz–Sobolev Spaces

We consider vector functions u: Rⁿ RN minimizing variational integrals of the form _ G (u) dx with convex density G whose growth properties are described in terms of an N -function A: (0, ) (0, ) with limsup ₓ A (t) t^–2 <. We then prove - under certain technical assumptions on G - full regularity of u provided that n = 2, and partial C¹ -regularity in the case n ≥ 3. The main feature of the paper is that we do not require any power growth of G.